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In mathematics Haboush's theorem, often still referred to as the Mumford conjecture, states that for any semisimple algebraic group G over a field K, and for any linear representation ρ of G on a K-vector space V, given v ≠ 0 in V that is fixed by the action of G, there is a G-invariant polynomial F on V, without constant term, such that F(v) ≠ 0.

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rdf:type	yago:WikicatTheoremsInRepresentationTheory yago:Abstraction100002137 yago:Communication100033020 yago:Message106598915 yago:Proposition106750804 motorsport season yago:Statement106722453 yago:Theorem106752293
rdfs:label	Haboush's theorem (en) Théorème de Haboush (fr)
rdfs:comment	In mathematics Haboush's theorem, often still referred to as the Mumford conjecture, states that for any semisimple algebraic group G over a field K, and for any linear representation ρ of G on a K-vector space V, given v ≠ 0 in V that is fixed by the action of G, there is a G-invariant polynomial F on V, without constant term, such that F(v) ≠ 0. (en) Le théorème de Haboush est un théorème par lequel William Haboush a démontré une conjecture de Mumford, établissant que pour tout groupe algébrique réductif G sur un corps k, pour toute représentation de G sur un k-espace vectoriel V, et pour tout vecteur non nul v dans V fixe par l'action de G, il existe sur V un polynôme G-invariant F tel que F(v) ≠ 0 et F(0) = 0. (fr)
dcterms:subject	Representation theory of algebraic groups Invariant theory Conjectures that have been proved Theorems in representation theory
Wikipage page ID	632762 (xsd:integer)
Wikipage revision ID	1051891084 (xsd:integer)
Link from a Wikipage to another Wikipage	David Mumford Representation theory of algebraic groups Vector space Mathematics Geometric invariant theory Invariant theory Ergebnisse der Mathematik und ihrer Grenzgebiete Steinberg representation Line bundle Semisimple algebraic group Field (mathematics) Conjectures that have been proved Advances in Mathematics Homogeneous polynomial Weyl's theorem on complete reducibility Borel subgroup Theorems in representation theory Polynomial Algebraically closed Weyl character formula G-invariant Very ample
Link from a Wikipage to an external page	http://projecteuclid.org/euclid.kjm/1250524787 http://www.numdam.org/item/SB_1974-1975__17__138_0/
sameAs	Haboush's theorem Haboush's theorem Haboush's theorem Haboush's theorem Haboush's theorem
dbp:wikiPageUsesTemplate	dbt:Springer dbt:Citation dbt:Cite_journal dbt:Harvtxt dbt:ISBN dbt:Short_description dbt:MathSciNet
authorlink	Vladimir L. Popov (en)
first	V.L. (en)
id	M/m065570 (en)
last	Popov (en)
title	Mumford hypothesis (en)
has abstract	In mathematics Haboush's theorem, often still referred to as the Mumford conjecture, states that for any semisimple algebraic group G over a field K, and for any linear representation ρ of G on a K-vector space V, given v ≠ 0 in V that is fixed by the action of G, there is a G-invariant polynomial F on V, without constant term, such that F(v) ≠ 0. The polynomial can be taken to be homogeneous, in other words an element of a symmetric power of the dual of V, and if the characteristic is p>0 the degree of the polynomial can be taken to be a power of p.When K has characteristic 0 this was well known; in fact Weyl's theorem on the complete reducibility of the representations of G implies that F can even be taken to be linear. Mumford's conjecture about the extension to prime characteristic p was proved by W. J. , about a decade after the problem had been posed by David Mumford, in the introduction to the first edition of his book Geometric Invariant Theory. (en) Le théorème de Haboush est un théorème par lequel William Haboush a démontré une conjecture de Mumford, établissant que pour tout groupe algébrique réductif G sur un corps k, pour toute représentation de G sur un k-espace vectoriel V, et pour tout vecteur non nul v dans V fixe par l'action de G, il existe sur V un polynôme G-invariant F tel que F(v) ≠ 0 et F(0) = 0. Le polynôme peut être choisi homogène, c'est-à-dire élément d'une puissance symétrique du dual de V, et si la caractéristique de k est un nombre premier p > 0, le degré du polynôme peut être choisi égal à une puissance de p. Pour k de caractéristique nulle, ce résultat était bien connu : dans ce cas, (en) de Weyl sur la complète réductibilité des représentations de G garantit même que F peut être choisi linéaire. L'extension aux caractéristiques p > 0, conjecturée dans l'introduction de a été démontrée par . (fr)
gold:hypernym	F
prov:wasDerivedFrom	wikipedia-en:Haboush's_theorem?oldid=1051891084&ns=0
page length (characters) of wiki page	8166 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Haboush's_theorem
is Link from a Wikipage to another Wikipage of	List of algebraic geometry topics List of conjectures Mumford conjecture David Mumford Emmy Noether Geometric invariant theory Steinberg representation Linear algebraic group Haboush William Haboush Reductive group Haboush theorem List of theorems
is Wikipage redirect of	Haboush theorem
is Wikipage disambiguates of	Haboush
is foaf:primaryTopic of	wikipedia-en:Haboush's_theorem

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